# Traveling faster than the speed of light?

• maxwilli06
In summary, the conversation discussed the inability to travel faster than the speed of light and the concept of relativity, where time and space can stretch to ensure this limit is not exceeded. The special properties of light were also mentioned, but the reason for its uniqueness is still unknown. The rules of relativity were derived by Einstein based on contradictions in 19th century science, and his theory has been proven through various experiments.
maxwilli06
I'm a total amateur so please don't judge my lack of knowledge. I'm a film major with a lot of interest in science.

So I know that it is not possible to travel faster that the speed of light. But I had this idea the other day:

If a capsule traveling at 99.9% of the speed of light and there is another object within this capsule, then it can still move forward right? And when it does, it is technically moving faster than the speed of light, right?

No. It's really wierd, time and space sort of stretch to make sure that nothing goes faster than the speed of light. Time can flow at different rates and even space can stretch for different objects. That's this ‘relativity’ thing.

When different objects, say space ships, are moving at different speeds (and the difference in speed is near light speed) from one space ship's perspective time is moving more slowly on the other spaceship and even distance looks different - the other spaceship seems to be squished and foreshortened.

The squishing of distance and slowing of time effects add up as you try to go faster so that in the end nothing travels faster than the speed of light.

And it's all proven to actually happen, for real: using really precise, synchronized clocks show the slowing of time for the clock that goes for a really high-speed trip, say flying around the world in an airplane. And it's been proven in other ways too.

Crazy, huh?

Just to follow up to your specific question, if, say, someone on one of those spaceships fired a gun so that you think the bullet ought to be going faster than the speed of light, from the other spaceship's view time would be moving more slowly and the distance the bullet covers would be squished enough that it would look like it was traveling a little bit faster, but not faster than the speed of light.

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maxwilli06 said:
I'm a total amateur so please don't judge my lack of knowledge. I'm a film major with a lot of interest in science.

So I know that it is not possible to travel faster that the speed of light. But I had this idea the other day:

If a capsule traveling at 99.9% of the speed of light and there is another object within this capsule, then it can still move forward right? And when it does, it is technically moving faster than the speed of light, right?

Let's say that your rocket travels at v=.999c with repect to you (the observer)
Let's say that your object inside the rocket travels at speed u with respect to the rocket.
Relativity tells us that the speed of the object with respect to you, is not $$v+u$$.
Surprisingly, it is:

$$w=\frac {u+v}{1+\frac {uv}{c^2}}$$

It is easy to show that $$w<c$$

Thanks so much. that makes perfect sense.

I do have one more question:

What is it about light that makes it so special? I don't understand why traveling faster than a photon would not be possible. Why light? Why not something else?

maxwilli06 said:
I do have one more question:

What is it about light that makes it so special? I don't understand why traveling faster than a photon would not be possible. Why light? Why not something else?

Good question, we don't know the answer to it. All existent experimental knowledge points that way. No exception to date. Maybe, one day, we'll find that there is "something else" :-)

I'm too a novice in case of relativity. From Wikipedia,

"Second postulate (SR) - Invariance of c - The speed of light in a vacuum is a universal constant, c, which is independent of the motion of the light source."

I.e., the speed of light is the same in all frame of reference regardless of their motion (i.e. in vaccum. Speed of light varies with optical density though.). Thus, that makes it special.

maxwilli06 said:
What is it about light that makes it so special? I don't understand why traveling faster than a photon would not be possible. Why light? Why not something else?

That's one I can't answer for you, I'm afraid, because I don't know the answer myself. I'm not a scientist, I just took some physics courses in college. I could tell you some stuff about the way light works but that wouldn't really answer the question. Hopefully someone else will come along and tell us.

In the mean time, I'll mention that one of the other interesting conclusions of relativity is that somehow gravity is just like accelerating really fast as far as stretching space and time. So time actually passes more quickly on mountaintops than it does down at sea level, believe it or not. Gravity also sort of “shrinks” space.

Imagine a box drawn around the sun, 2 trillion miles on a side. In empty or “flat” space, without a gravity source in it, that box would contain 2³ = 8 trillion trillion cubic miles of space. But because of the deforming / stretching effect of the sun's gravity, within the same area marked off around the sun there's less than 8 trillion trillion cubic miles of space.

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then how did these rules of relativity come to be?

Einstein was so smart that from small contradictions in 19th century science, he figured out that it had to be true.

The legend is that when he was a teenager he read a science book that contained an example where the reader was asked to imagine he was a telegraph signal, traveling down the telegraph wire at the speed of light. Einstein kept thinking about that as he grew up and as he learned more physics he realized that some things, like electromagnetism, wouldn't work properly if material objects could travel at the same speed as light.

He also took into account things like the fact that the planet Mercury moves wrong as it orbits the sun - its path curves too much, because of that stretching of space phenomenon I mentioned before. With Einstein's general relativity rules he was able to predict exactly how much the curve of Mercury's orbit would be off and astronomers were able to confirm that he was precisely correct.

It's important to note that we could just all be stupid hairless monkeys. There may be little grey aliens somewhere laughing their butts off at us because we think these things have anything to do with the speed of light; that might just be a coincidence. But the theories of relativity that Einstein gave us a hundred years ago are the best we've got right now and they predict and explain the outcomes of many experiments we do and many phenomena we see.

I'm so confused cause I've been trying to read up on relativity.

Basically I've come to understand that during motion one cannot differentiate which object is moving. So then what is to say that we are not moving through light while the photons stay still?

maxwilli06 :
So then what is to say that we are not moving through light while the photons stay still?
We would need to be moving in every direction at once, which is impossible.

maxwilli06 said:
I do have one more question:

What is it about light that makes it so special? I don't understand why traveling faster than a photon would not be possible. Why light? Why not something else?

it's a good question that has been asked before. it's not just light. light is the propagation of a disturbance of an electric field. but any other fundamental force (like gravity or the nuclear forces) need no medium to propagate and do so at the same speed. it is not so much about light or EM fields, it's about the nature of space and time that these ostensibly "instantaneous" actions actually propagate at a finite speed.here is the thread where we were talking about this before: https://www.physicsforums.com/showthread.php?p=1556816#post1556816

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maxwilli06 said:
I'm so confused cause I've been trying to read up on relativity.

Basically I've come to understand that during motion one cannot differentiate which object is moving. So then what is to say that we are not moving through light while the photons stay still?

As you say you can't differentiate which object is moving. But light always moves at the speed of light¹ and it is not affected by relativistic affects. The movement of light is not squished or deformed, it appears the same to all observers. This can seem counterintuitive but it's the main reason why everything else seems weird and involves complicated math.

I won't pretend to know why it's this way and I'm not entirely sure science has a deeper answer (though it might, it seems like you have to go pretty deep before you can even expect to understand simply the titles of all the relevant books and papers) but these phenomena are consistent with each other in the understanding I've achieved so far.

¹ In “free space” at least, which means to say that light in air or water or glass moves more slowly because it interacts with those materials to some degree even though they're transparent.

Thanks for that note rbj. I had realized that gravity must propagate at the same speed as light but I'd never made that connection that it's a constraint on all of the fundamental forces.

maxwilli06 said:
I'm so confused cause I've been trying to read up on relativity.

Basically I've come to understand that during motion one cannot differentiate which object is moving. So then what is to say that we are not moving through light while the photons stay still?
When physicists say "one cannot differentiate which object is moving" they are talking about the fact that in SR, every object's reference frame is equally valid, and in my rest frame you'd be the one who's moving while in your rest frame I'd be the one who's moving. But light does not have its own rest frame in SR--this would violate one of the postulates of relativity which says the laws of physics should work the same in every frame (in the frame of a sublight object you can never see a photon at rest), and the coordinates used by different frames are supposed to represent the readings of actual rulers and clocks at rest in that frame (so if one object is at position x=5 meters in my frame and another object is at position x=7 meters, a ruler at rest in my frame would measure a distance of 2 meters between them), but it's impossible to have rulers and clocks moving at light speed.

Now that I've read through it totally awesome [post=1556816]post[/post] on this subject rjb. He has articulated a deeper reason for the constraint on the speed of light etc., everyone.

The one note I'll make, which you're probably already aware of, is where you say

rjb said:
…from that, we got time dilation, then length contraction, then Lorentz transformation, and so on.

You may be aware that the Lorentz transformations preceded Special Relativity itself - if you refer to the historical note at the top of the http://en.wikipedia.org/wiki/Lorentz_transformation" article.

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K I'm slowly understanding this.

If two objects are moving in opposite directions parallel to a beam of light, then for the object moving in the direction of the beam time speeds, and for the object moving against the beam time slows? in order to keep c constant in relation to different refrences?

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So technically the faster you are moving the more you are slowing down time surrounding you and thus traveling forward in time.

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AH! but then isn't time relative to? What is to say that I am speeding in time or the rest of the world is slowing?

maxwilli06 said:
K I'm slowly understanding this.

If two objects are moving in opposite directions parallel to a beam of light, then for the object moving in the direction of the beam time speeds, and for the object moving against the beam time slows? in order to keep c constant in relation to different refrences?

Not quite. They both see the beam of light moving in the same manner (in the same direction and covering the same distance by their own clocks and their own rulers) but they each think that the other one is slowed down and squished.

CaptainQuasar said:
Not quite. They both see the beam of light moving in the same manner (in the same direction and covering the same distance by their own clocks and their own rulers) but they each think that the other one is slowed down and squished.
?

So I'm going to try an explain my logic for how i came up with that, because I'm still not understanding this.

If an object is moving next to a beam of light, it seems as though the faster you move, the easier it is to see individual photons (which is obviously not true). However, since the speed of the beam is constant in relation to any reference frame, time has to compensate by slowing down the object's time in order to keep light moving at the constant speed. Meaning the faster you move, the more time has the compensate by slowing down, meaning the quicker you travel into the future.

Now if the same object is traveling against a beam of light, it seems as though it would be harder to pick out individual photons( also no true.) So, inorder to compensate, the object's time has to speed up. Meaning the object ages faster in relation to its surroundings.

That's how i came to that.
Oh, and what do you mean by squished?
Also, do you have any books to suggest, so I can stop bugging people?

maxwilli06 said:
If an object is moving next to a beam of light, it seems as though the faster you move, the easier it is to see individual photons (which is obviously not true)

I think what might be confusing the issue is that you can't “catch up” to a beam of light. No matter how hard or how long you accelerate in the same direction a beam of light is going in it still appears to be moving at 299792458 m/s to you. Similarly if you accelerate in the direction a beam of light is coming from it does not appear to be moving faster.

You might think that this will cause it to appear that light passes different objects at different times for different observers. But not so, that's what all the stretching and deformation of time and space fixes.

maxwilli06 said:
Oh, and what do you mean by squished?

I'm talking about the relativistic phenomenon that is known as http://en.wikipedia.org/wiki/Length_contraction" , with the axis of symmetry parallel to the direction of travel.

maxwilli06 said:
Also, do you have any books to suggest, so I can stop bugging people?

I don't, sorry. I have had to put this all together from studying physics at school and many different books and web sites.

These are great questions though. I really think that introductions to special relativity should start with things like this and leave the equations and everything for later on.

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CaptainQuasar said:
I think what might be confusing the issue is that you can't “catch up” to a beam of light. No matter how hard or how long you accelerate in the same direction a beam of light is going in it still appears to be moving at 299792458 m/s to you. Similarly if you accelerate in the direction a beam of light is coming from it does not appear to be moving faster.

You might think that this will cause it to appear that light passes different objects at different times for different observers. But not so, that's what all the stretching and deformation of time and space fixes.

Right this is what I was trying to say: although it seems like you would be able to see and catch up to a beam, you can't. which is what i meant when I said time has to bend in order to keep that light moving at the same speed from the perspective of that object. Am I getting this?

Oh, yes, I see now. Yeah, I think you're getting it.

i was reading this thread and i thought, what light are we talking?sunlight? can we consider light from other sources, like lasers, lamps, etc.
Are they all the "same"?

tko_gx said:
i was reading this thread and i thought, what light are we talking?sunlight? can we consider light from other sources, like lasers, lamps, etc.
Are they all the "same"?
It doesn't matter, all light travels at c in a vacuum.

Could you explain to me in more detail the relation of Mercury's orbit with the stretching of space??

This is technically referred to as the http://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury". Mercury's orbit around the sun is approximately a circle, right? Really an ellipse.

With classical physics astronomers can calculate exactly how big the ellipse that Mercury traces around the sun with its orbit should be based on the masses of the sun and other planets and the force of gravity calculated based upon those masses. But because of the general relativity effects the immense mass of the sun actually shrinks the space around it, something like the length contraction effect from near-c speeds. So the circumference of the ellipse - the distance that Mercury has to go to make one orbit around the sun - is slightly shorter than it should be and so Mercury moves in a sort of corkscrew or http://en.wikipedia.org/wiki/Hypotrochoid" pattern.

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CaptainQuasar said:
This is technically referred to as the http://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury". Mercury's orbit around the sun is approximately a circle, right? Really an ellipse.

With classical physics astronomers can calculate exactly how big the ellipse that Mercury traces around the sun with its orbit should be based on the masses of the sun and other planets and the force of gravity calculated based upon those masses. But because of the general relativity effects the immense mass of the sun actually shrinks the space around it, something like the length contraction effect from near-c speeds. So the circumference of the ellipse - the distance that Mercury has to go to make one orbit around the sun - is slightly shorter than it should be and so Mercury moves in a sort of corkscrew or http://en.wikipedia.org/wiki/Hypotrochoid" pattern.

So the more gravity there is, the more space and time are bent? and if they are are they bent unanimously? I guess this gets into the other part of general relativity. I'm trying to figure out how gravity bends time. and at what point does it stop time completely.

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maxwilli06 said:
So the more gravity there is, the more space and time are bent?

Yes…

maxwilli06 said:
and if they are are they bent unanimously?

…but I don't get what you mean by that.

maxwilli06 said:
I'm trying to figure out how gravity bends time. and at what point does it stop time completely.

I don't know exactly how gravity does it. I know that merely describing the precise way in which gravity bends space and time involves something called tensor calculus. Tensor calculus is some sort of unholy miscegenation of multivariable calculus and matrix algebra. Just thinking about that gives me the willies.

As far as stopping time, I think you start to run into something like that with black holes.

change in frequency

maxwilli06 said:
If an object is moving next to a beam of light, it seems as though the faster you move, the easier it is to see individual photons (which is obviously not true). … Now if the same object is traveling against a beam of light, it seems as though it would be harder to pick out individual photons( also not true.)

Actually, it is true! If you move in the same direction as a beam of light (in other words, away from the source), then it is easier to see individual photons - a flashing light will appear to flash slower. Similarly, the wavelength will become longer, the frequency will be lower, and the light will be redder ("red-shifted"), and you will say that the light has lost energy.

If you move in the opposite direction, it is harder to pick out individual photons (they come "thicker and faster"), and so a flashing light will appear to flash faster, the frequency will be higher, and similarly the light will be blue-shifted, and you will say that the light has gained energy.

If you relative to any object, you will notice a change in its energy.

For a slower-than-light object, this change in energy is mostly because of the change in its speed, and only slightly because of an apparent internal effect, which we choose to call an "change in mass".

But, for light itself, there is no change in its speed, and so the change in energy is entirely because of an apparent internal effect, which we choose to call a "change in frequency (or colour)".

Light stays the same speed, but changes colour.

However, since the speed of the beam is constant in relation to any reference frame, time has to compensate by slowing down the object's time in order to keep light moving at the constant speed. Meaning the faster you move, the more time has the compensate by slowing down, meaning the quicker you travel into the future.

Yes, but this has nothing to do with whether there happens to be some light going past you. You could have light going past you in two opposite directions, and yet you only have one clock! Your time "slowing down" has nothing to do with your speed or direction relative to light, but only relative to whoever is watching you and saying "ooh look, his time has slowed down!"

Faster than Light

Now I know no object object as yet observed by science can move faster that the speed of light (SOL), you did a very good job of explaining that.

But what would happen if we could see a spaceship moving faster than light?

Lets say we have a telescope that can see a spaceship traveling between two stars 10 light years away and that we, the observers, are on Earth directly between the stars but not quite (Just enough room for the ship to pass by us). Let's say this ship moves so fast that it only takes a few minutes to get from one star to the other.

Ive been racking my brain of what it would look like. If I am thinking correctly if the object goes from a distant star to the Earth, the spacecraft would beat its own light beams from when it was at the star. When the ship reaches us it would seem to just appear but simutaniously we would see the ship moving backward twards the first star, forwards twards the second star, and if the ship were in orbit around the first star being constructed for many years we would see that image too, all three images of the same thing at the same time. After the ship passes us It would just seem to be moving very fast away from us until it reached the second star.

Is this right?
I know the image of an object approaching the SOL is squished but what about those moving faster than the SOL?
What happens when the image of the ship traveling backwards twards the 1st star meets the image of the ship just before it leaves the star? Does it just disappear?
And what do we observe as the ship accelerates above the SOL, and then decelerates below the SOL?

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Welcome to PF!

Magnetron said:
{snip} When the ship reaches us it would seem to just appear but simutaniously we would see the ship moving backward twards the first star, forwards twards the second star, and if the ship were in orbit around the first star being constructed for many years we would see that image too, all three images of the same thing at the same time. {snip}

Hi Magnetron! Welcome to PF!

Everything you describe (which sounds about right) is an optical illusion, rather like looking at something moving past a warped mirror, and seeing two images of it appear out of nothing in the middle of the mirror, and move apart!

But in relativity (and in reality), we compensate for the speed of light being finite.

When we look at a distant star or galaxy, we are well aware that we are "looking at the past", and we make allowance for that in deciding what is the time of whatever we are looking at.

So when we see your spaceship appear from nowhere, and then move both forward and backward, it doesn't bother us … we know it's only an illlusion, which doesn't affect our maths!

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